Problem: A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$5.00$, and bags of cookies cost $$3.50$, and sales equaled $$48.00$ in total. There were $4$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Solution: Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${5x+3.5y = 48}$ ${y = x+4}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+4}$ for $y$ in the first equation. ${5x + 3.5}{(x+4)}{= 48}$ Simplify and solve for $x$ $ 5x+3.5x + 14 = 48 $ $ 8.5x+14 = 48 $ $ 8.5x = 34 $ $ x = \dfrac{34}{8.5} $ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $ {y = x+4}$ to find $y$ ${y = }{(4)}{ + 4}$ ${y = 8}$ You can also plug ${x = 4}$ into $ {5x+3.5y = 48}$ and get the same answer for $y$ ${5}{(4)}{ + 3.5y = 48}$ ${y = 8}$ $4$ bags of candy and $8$ bags of cookies were sold.